Time series

Load data

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Define period for vector to learn in first signal

period_start_1 <- "2019-02-12 03:38:00" # YYYY-MM-DD hh:mm:ss
period_end_1 <- "2019-02-12 03:46:00" # YYYY-MM-DD hh:mm:ss

Define period from second signal where to find learned signal

period_start_2 <- "2019-02-24 12:00:00" # YYYY-MM-DD hh:mm:ss
period_end_2 <- "2019-02-24 20:00:00" # YYYY-MM-DD hh:mm:ss

step_size = 4 # step size for discretization in seconds

Chosen time period for signals

Statistics table

Some statistics explained:

Signal length - Data points number in signal
Time mode - Mode of time change frequency
Value mode - Most frequent value
Sd - Standard deviation
Mean - Average value
n5, n25, n75, n95 - Quantile values
Kurtosis - Kurtosis quantifies the peak value of the PDF (positive kurtosis tells that there is lot of data in tails, negative - little data in tails
Skewness - Skewness quantifies the asymmetry behavior of vibration signal through its PDF
RMS - Root mean square value changes faster then mean
Entropy - Amount of uncertainty in an entire probability distribution
Crest factor (cf) - Ratio of the instantaneous peak amplitude of a waveform, to its root mean square RMS value
Shape factor (sf) - Shape factor is a value that is affected by an object’s shape but is independent of its dimensions
Mean crossing - Mean value crossing count

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Data discretization

Data was discretized every 4 seconds

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Generalized Additive Model

Generalized additive model formula:

• \(g(E(Y)) = \beta_{0} + f_{1}(x_{1}) + f_{2}(x_{2}) + \cdots + f_{m}(x_{m}) + \varepsilon\)
  • \(x_{1}, x_{2}, \dots, x_{m}\) - are independent variables
    
  • \(\beta_{0}\) - is an intercept
    
  • \(f_{1}, f_{2}, \dots, f_{m}\) - are unknow smooth functions (splines)
    
  • \(\varepsilon\) - is an random error

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In our case formula is :

• \(g(E(Y)) = \beta_{0} + f_{1}(x_{1}) + \varepsilon\),

  • \(f(x_{1})=\sum_{j=1}^{k}b_{j}(x_{1}) \beta_{j}\),
    
  • \(b_{j}(x_{1}) \beta_{j}\) - smooth spline function.

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Correlation

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